1 Supplement 1. Systematic review results

1.1 PRISMA flowchart

Donne moi les chiffres quand tu as fini, j’insèrerai

PRISMAstatement::prisma(found = 750,
       found_other = 123,
       no_dupes = 776, 
       screened = 776, 
       screen_exclusions = 13, 
       full_text = 763,
       full_text_exclusions = 17, 
       qualitative = 746, 
       quantitative = 319,
       width = 800, height = 1200)

1.2 N studies (adjustment discarded)

dat_out_agg %>%
    group_by(outcome_RDoC_agg) %>%
    summarise(n_exp = sum(n_exp_out),
              n_nexp = sum(n_nexp_out),
              nstudy1 = n(),
              n_study2 = length(unique(ID_prec)))
## # A tibble: 4 x 5
##   outcome_RDoC_agg                      n_exp n_nexp nstudy1 n_study2
##   <chr>                                 <dbl>  <dbl>   <int>    <int>
## 1 Mixed social processes                 6192   5843      87       87
## 2 Reception of facial communication      2785   3124      45       45
## 3 Reception of non-facial communication   539    732       9        9
## 4 Understanding mental states            2818   2650      60       60

1.3 N studies (adjustment splitted)

synth_n = dat_out %>%
    group_by(outcome_RDoC) %>%
    summarise(n_exp = sum(n_exp_out),
              n_nexp = sum(n_nexp_out),
              nstudy1 = n(),
              n_study2 = length(unique(ID_prec)))
synth_n
## # A tibble: 8 x 5
##   outcome_RDoC                                      n_exp n_nexp nstudy1 n_stu~1
##   <chr>                                             <dbl>  <dbl>   <int>   <int>
## 1 Mixed social processes (adjusted)                   277    306       8       8
## 2 Mixed social processes (non-adjusted)              6046   5685      82      82
## 3 Reception of facial communication (adjusted)       1064   1577       7       7
## 4 Reception of facial communication (non-adjusted)   1873   1703      41      41
## 5 Reception of non-facial communication (adjusted)    261    542       3       3
## 6 Reception of non-facial communication (non-adjus~   351    254       7       7
## 7 Understanding mental states (adjusted)              245    274       9       9
## 8 Understanding mental states (non-adjusted)         2712   2536      56      56
## # ... with abbreviated variable name 1: n_study2

2 Supplement 2. ES visualization

2.1 Distribution of ES

ggplot(dat.meta, aes(x = es_adj, y = es)) + 
  geom_jitter(alpha = 0.3, width = 0.35, size = 2) +
    geom_violin(size = 0.5, alpha = 0.5) +
theme_bw() 

2.2 Distribution of ES / outcomes

2 plots, tu choisis celui qui tu préfères

ggplot(dat.meta, aes(x = outcome_RDoC_agg, y = es)) + 
       geom_jitter(width = 0.05, dotsize = 0.1, alpha = 0.2, aes(fill = ID)) +        geom_boxplot(trim=FALSE, alpha = 0.6) +
      facet_grid(es_adj ~ "") +
       theme_bw() +
      labs(y = "Standardized mean difference (SMD)", x = "") +
        guides(fill=FALSE) +
       coord_flip()

ggplot(dat.meta, aes(x = outcome_RDoC_agg, y = es)) + 
    geom_violin(aes(fill = outcome_RDoC_agg), alpha = 0.3) +
  geom_jitter(alpha = 0.2, width = 0.1) +
    geom_boxplot(width=0.1)+
    facet_grid(es_adj ~ "") +
    theme_bw() +
    labs(y = "Standardized mean difference (SMD)", x = "") +
    theme(text = element_text(size = 18),
          legend.position = "none",
          axis.title.y = element_text(size=12, face="bold"), 
          axis.title.x = element_text(size=12, face="bold")) +
    coord_flip()  


3 Supplement 3. Main analysis

3.1 Data analysis

V.SCE  <- with(dat.meta,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study, 
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = outcome_RDoC))

# all.equal(dat.meta$se^2, diag(unlist(V.SCE)))

SCE <- metafor::rma.mv(yi = es, V = V.SCE, 
                       data = dat.meta, 
                       mods = ~ outcome_RDoC - 1,
                       random = ~ outcome_RDoC | ID_study,
                       struct = "DIAG",
                       sparse = TRUE)

SCE.ISQ <- metafor::rma.mv(yi = es, V = V.SCE, 
                       data = dat.meta, 
                       mods = ~ outcome_RDoC - 1)
het = function(x, y) {
  i2 = NA
  for (i in 1:nrow(vcov(x))) {
    i2[i] = 100 * (vcov(x)[i,i] - vcov(y)[i,i]) / vcov(x)[i,i]
  }
  return(i2)
}
# 
# W <- solve(V.SCE)
# X <- model.matrix(SCE)
# P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W
# 100 * SCE$tau2 / (SCE$tau2 + (SCE$k-SCE$p)/sum(diag(P)))


res.SCE <- data.frame(clubSandwich::coef_test(SCE, vcov = "CR2", cluster = dat.meta$ID_study)) # , cluster = df.ES$researchgroup
res.SCE.ci = data.frame(clubSandwich::conf_int(SCE, vcov = "CR2", cluster = dat.meta$ID_study))
res.SCE$target <- gsub("outcome_RDoC", "", row.names(res.SCE))
res.SCE.ci$target <- gsub("outcome_RDoC", "", row.names(res.SCE.ci))
res.SCE = dplyr::left_join(res.SCE, res.SCE.ci)
res.SCE$I2 = het(SCE, SCE.ISQ)
res_main <- left_join(res.SCE, dat_RDoC)
## Joining, by = "target"
res_main[,c("beta", "SE", "tstat", "df", "p_Satt", "CI_L", "CI_U", "I2", "n_studies",    "n_nexp_out" , "n_exp_out")] <- apply(res_main[,c("beta", "SE", "tstat", "df", "p_Satt", "CI_L", "CI_U", "I2", "n_studies",    "n_nexp_out" , "n_exp_out")], 2, function(x) round(x, 3))
DT::datatable(res_main, 
              rownames = FALSE,
              extensions = 'Buttons',
              options = list(  # options
                buttons = c('copy', 'excel'),
                scrollX = TRUE,
                dom = c('ftB'), 
                autoWidth = TRUE,
                columnDefs = list(
                  list(className = 'dt-center', 
                                     targets = "_all"))))

3.2 Forest plot

res_main$SE_COR = (res_main$CI_U - res_main$CI_L) / 3.92

res_main$raw_outcome <- gsub(r"{\s*\([^\)]+\)}","",
                            as.character(res_main$outcome_RDoC))
tab.plot <- data.frame(
  Outcome = do.call(rbind, lapply(res_main$outcome_RDoC, 
                                  function(x) paste(strwrap(x, width = 60), 
                                                    collapse = "\n"))),
  n_ADHD = res_main$n_exp_out,
  n_nexpT = res_main$n_nexp_out,
  n_studies = res_main$n_studies,
  I2 = paste0(round(res_main$I2), "%"))

value_num_plot = data.frame(apply(res_main[, c("beta", "SE_COR")], 2, function(x) as.numeric(as.character(x))))

forest_modif(x = value_num_plot[ ,c("beta", "SE_COR")], 
           variant = "classic",
           col = "Greys", xlab = "SMD", annotate_CI = TRUE,
           study_table = tab.plot,
           group = res_main$raw_outcome,
           type = "study_only",
           text_size = 3.5,
           x_limit = c(-1, 2),
           N = tab.plot$n_ADHD + tab.plot$n_nexpT,
           x_breaks = seq(-3, 3, 1)
           )

3.3 Diagnostics

# windows() ## create window to plot your file
# metafor::profile.rma.mv(SCE)
# dev.off()

4 Supplement 4. Supplementary analyses

4.1 S1. Borenstein aggregated approach

meta.reg <- metafor::rma.mv(yi = es, V = se^2, 
                           data = dat.borenstein, 
                           random = ~ outcome_RDoC | ID_study,
                           struct = "DIAG",
                           mods = ~ outcome_RDoC - 1)
meta.reg$beta = round(meta.reg$beta, 3)
meta.reg$se = round(meta.reg$se, 3)
meta.reg$pval = round(meta.reg$pval, 3)
res.S1.clean = data.frame(
  beta = meta.reg$beta,
  se = meta.reg$se,
  pval = meta.reg$pval, 
  target = gsub("outcome_RDoC", "", row.names(meta.reg$b)))

res.S1 <- left_join(res.S1.clean, dat_RDoC)
## Joining, by = "target"
DT::datatable(res.S1, 
              rownames = FALSE,
              extensions = 'Buttons',
              options = list(  # options
                buttons = c('copy', 'excel'),
                scrollX = TRUE,
                dom = c('ftB'), 
                autoWidth = TRUE,
                columnDefs = list(
                  list(className = 'dt-center', 
                                     targets = "_all"))))

4.2 S2. RVE approach

robu.main <- robumeta::robu(es ~ outcome_RDoC - 1, 
                            data = dat.meta, 
                            studynum = ID_study,
                            var.eff.size = se^2,
                            modelweights = "CORR",
                            small = TRUE,
                            rho = 0.8)
dat_robu_main = cbind(
  robu.main$reg_table$labels,
  round(robu.main$reg_table[,2:(ncol(robu.main$reg_table) -1)], 3))
DT::datatable(dat_robu_main, 
              rownames = FALSE,
              extensions = 'Buttons',
              options = list(  # options
                buttons = c('copy', 'excel'),
                scrollX = TRUE,
                dom = c('ftB'), 
                autoWidth = TRUE,
                columnDefs = list(
                  list(className = 'dt-center', 
                                     targets = "_all"))))

4.3 S3. Small study effects & ESS

Nakaraga method

dat.meta$inv_n_tilda <- with(dat.meta, (n_nexp + n_exp)/(n_nexp*n_exp))
dat.meta$sqrt_inv_n_tilda <- with(dat.meta, sqrt(inv_n_tilda))

nak.pb = metafor::rma.mv(yi = es, V = V.SCE, 
                      data = dat.meta, 
                      mods = ~ 1 + sqrt_inv_n_tilda + outcome_RDoC,
                      random = ~ outcome_RDoC | ID_study,
                      struct = "DIAG",
                      sparse = TRUE)
clubSandwich::coef_test(nak.pb, vcov = "CR2", cluster = dat.meta$ID_study)
##                                                              Coef. Estimate
## 1                                                          intrcpt    0.131
## 2                                                 sqrt_inv_n_tilda    5.218
## 3                outcome_RDoCMixed social processes (non-adjusted)   -0.116
## 4         outcome_RDoCReception of facial communication (adjusted)   -0.712
## 5     outcome_RDoCReception of facial communication (non-adjusted)   -0.790
## 6     outcome_RDoCReception of non-facial communication (adjusted)   -0.688
## 7 outcome_RDoCReception of non-facial communication (non-adjusted)   -0.975
## 8               outcome_RDoCUnderstanding mental states (adjusted)   -0.851
## 9           outcome_RDoCUnderstanding mental states (non-adjusted)   -0.619
##      SE t-stat  d.f. p-val (Satt) Sig.
## 1 0.530  0.247  8.94      0.81079     
## 2 1.919  2.719 17.93      0.01411    *
## 3 0.256 -0.451  8.45      0.66310     
## 4 0.309 -2.303 11.64      0.04056    *
## 5 0.264 -2.990  9.40      0.01449    *
## 6 0.372 -1.850  3.92      0.13935     
## 7 0.272 -3.591  9.60      0.00525   **
## 8 0.315 -2.701  9.78      0.02267    *
## 9 0.258 -2.400  9.51      0.03849    *

PET/PEET method (Stanley 2014)

PET = metafor::rma.mv(yi = es, V = V.SCE, 
                      data = dat.meta, 
                      mods = ~ se^2,
                      random = ~ outcome_RDoC | ID_study,
                      struct = "DIAG",
                      sparse = TRUE)
clubSandwich::coef_test(PET, vcov = "CR2", cluster = dat.meta$ID_study)
##     Coef. Estimate    SE t-stat d.f. p-val (Satt) Sig.
## 1 intrcpt    -2.89 0.454  -6.36 71.9       <0.001  ***
## 2      se    14.46 1.694   8.53 24.6       <0.001  ***

Egger’s test + ESS

dat_ess = data.frame(
  meta_review = "Haza",
  study = dat.borenstein$ID_study,
  factor = dat.borenstein$outcome_RDoC,
  value = dat.borenstein$es,
  se = dat.borenstein$se,
  n_cases = dat.borenstein$n_exp,
  n_controls = dat.borenstein$n_nexp,
  measure = "G")
  
umb = metaumbrella::umbrella(dat_ess)
## Analyzing factor: Understanding mental states (non-adjusted) 
## Analyzing factor: Mixed social processes (non-adjusted) 
## Analyzing factor: Mixed social processes (adjusted) 
## Analyzing factor: Understanding mental states (adjusted)
## - An error occured when converting the standard error of G to SMD. The standard error of the SMD was assumed to be equal to 'sqrt(1/n_cases + 1/n_controls)'.
## Analyzing factor: Reception of facial communication (non-adjusted) 
## Analyzing factor: Reception of non-facial communication (non-adjusted)
## - An error occured when converting the standard error of G to SMD. The standard error of the SMD was assumed to be equal to 'sqrt(1/n_cases + 1/n_controls)'.
## Analyzing factor: Reception of facial communication (adjusted) 
## Analyzing factor: Reception of non-facial communication (adjusted)
umb
## 
## Umbrella review:
##                                                 Factor n_studies total_n
## 1           Understanding mental states (non-adjusted)        56    4917
## 2                Mixed social processes (non-adjusted)        82   10770
## 3                    Mixed social processes (adjusted)         8     583
## 4               Understanding mental states (adjusted)         9     519
## 5     Reception of facial communication (non-adjusted)        41    3168
## 6 Reception of non-facial communication (non-adjusted)         7     605
## 7         Reception of facial communication (adjusted)         7    1075
## 8     Reception of non-facial communication (adjusted)         3     497
##   n_cases n_controls measure value       value_CI    eG          eG_CI   eOR
## 1    2521       2396       G 0.835  [0.68, 0.989] 0.835  [0.68, 0.989] 4.544
## 2    5570       5200       G 1.055 [0.908, 1.201] 1.055 [0.908, 1.201] 6.773
## 3     277        306       G 1.257 [0.607, 1.908] 1.257 [0.607, 1.908] 9.782
## 4     245        274       G 0.879 [0.455, 1.304] 0.879 [0.455, 1.304] 4.928
## 5    1657       1511       G 0.789 [0.603, 0.974] 0.789 [0.603, 0.974] 4.181
## 6     351        254       G 0.968 [0.525, 1.411] 0.968 [0.525, 1.411] 5.784
## 7     425        650       G 0.557 [0.355, 0.759] 0.557 [0.355, 0.759] 2.747
## 8     171        326       G 0.590 [0.008, 1.172] 0.590 [0.008, 1.172] 2.917
##            eOR_CI  p_value     I2           PI_eG          PI_eOR  egger_p
## 1  [3.433, 6.015] 3.62e-26 84.410 [-0.239, 1.908] [0.648, 31.844] 6.18e-01
## 2  [5.194, 8.832] 2.70e-45 88.405  [-0.201, 2.31] [0.695, 66.008] 1.07e-04
## 3 [3.008, 31.817] 1.51e-04 91.236 [-1.084, 3.598] [0.14, 683.241] 2.73e-01
## 4 [2.283, 10.638] 4.87e-05 79.001 [-0.607, 2.366] [0.332, 73.049] 1.45e-01
## 5  [2.986, 5.852] 7.75e-17 86.138  [-0.333, 1.91] [0.547, 31.979] 4.46e-01
## 6   [2.59, 12.92] 1.86e-05 82.754  [-0.515, 2.45] [0.393, 85.127] 8.53e-01
## 7  [1.903, 3.965] 6.77e-08 55.000 [-0.024, 1.138]  [0.958, 7.875] 4.78e-01
## 8  [1.015, 8.385] 4.69e-02 77.993 [-6.381, 7.561] [0, 904222.896] 7.65e-01
##      ESB_p power_med     JK_p   largest_CI_eG  largest_CI_eOR rob amstar
## 1 9.90e-01       100 5.37e-25 [-0.304, 0.449]  [0.576, 2.258]  NA     NA
## 2 1.00e-01       100 6.07e-44 [-0.154, 0.883]  [0.757, 4.957]  NA     NA
## 3 6.73e-01       100 1.53e-03  [0.623, 1.315] [3.095, 10.864]  NA     NA
## 4 3.78e-01       100 3.44e-04  [0.271, 0.939]  [1.634, 5.494]  NA     NA
## 5 7.50e-01       100 8.10e-16  [1.259, 1.804] [9.805, 26.349]  NA     NA
## 6 3.58e-01       100 6.06e-04  [0.967, 1.419] [5.776, 13.118]  NA     NA
## 7 2.37e-01       100 6.53e-06   [0.218, 1.22]   [1.484, 9.15]  NA     NA
## 8 4.14e-01       100 2.32e-01  [0.165, 0.879]  [1.348, 4.928]  NA     NA
# metaumbrella::umbrella(subset(dat_ess, factor == "Mixed social processes (non-adjusted)"))[[1]]$egger$p.value
# metafor::regtest(x = dat_sub$es, sei = dat_sub$se, model = "lm", predictor="sei")$pval

Plot

ggplot(dat.borenstein, aes(x=es, y=se)) + 
    geom_point(alpha = 0.2) + 
    geom_smooth(method="lm") + 
    facet_wrap(~outcome_RDoC, scales='free') +
    theme_bw()
## `geom_smooth()` using formula 'y ~ x'

4.4 S4. type of publication

SCE.S2 <- metafor::rma.mv(yi = es, V = V.SCE, 
                       data = dat.meta, 
                       mods = ~ type_publication - 1 + outcome_RDoC,
                       random = ~ outcome_RDoC | ID_study,
                       struct = "CS",
                       sparse = TRUE)

clubSandwich::coef_test(SCE.S2, vcov = "CR2", cluster = dat.meta$ID_study)
##                                                               Coef. Estimate
## 1                                           type_publicationArticle    1.340
## 2                                        type_publicationConférence    3.532
## 3                                            type_publicationPoster    0.986
## 4                                             type_publicationThèse    1.398
## 5                 outcome_RDoCMixed social processes (non-adjusted)   -0.123
## 6          outcome_RDoCReception of facial communication (adjusted)   -0.798
## 7      outcome_RDoCReception of facial communication (non-adjusted)   -0.734
## 8      outcome_RDoCReception of non-facial communication (adjusted)   -0.777
## 9  outcome_RDoCReception of non-facial communication (non-adjusted)   -0.962
## 10               outcome_RDoCUnderstanding mental states (adjusted)   -0.594
## 11           outcome_RDoCUnderstanding mental states (non-adjusted)   -0.568
##       SE t-stat  d.f. p-val (Satt) Sig.
## 1  0.196  6.828  7.15      < 0.001  ***
## 2  0.204 17.314  7.85      < 0.001  ***
## 3  0.334  2.949  1.50      0.13694     
## 4  0.213  6.567 12.55      < 0.001  ***
## 5  0.204 -0.601  7.85      0.56489     
## 6  0.194 -4.122  9.82      0.00215   **
## 7  0.204 -3.603  9.72      0.00505   **
## 8  0.252 -3.083  3.46      0.04467    *
## 9  0.210 -4.583 12.68      < 0.001  ***
## 10 0.208 -2.852  7.92      0.02164    *
## 11 0.202 -2.813  8.44      0.02158    *
ggplot(dat.borenstein, aes(x = type_publication, y = es)) + 
  geom_point(size = 3, alpha = 0.2) + 
  geom_boxplot() +
  theme_bw()

4.5 S5. Each facial emotion

4.5.1 Data analysis

dat.meta.S3 = subset(dat.meta, 
    emot_spec %in% c("Happy", "Sad", "Surprise", "Fear", "Disgust", "Anger") & 
      grepl("Reception of facial", dat.meta$outcome_RDoC, fixed = TRUE) & 
      !grepl("(adjusted)", dat.meta$outcome_RDoC, fixed = TRUE))

V.SCE.S3  <- with(dat.meta.S3,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study,
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = emot_spec))

# all.equal(dat.meta$se^2, diag(unlist(V.SCE)))

SCE.S3 <- metafor::rma.mv(yi = es, V = V.SCE.S3, 
                       data = dat.meta.S3, 
                       mods = ~ emot_spec - 1,
                       random = ~ emot_spec | ID_study,
                       struct = "CS",
                       sparse = TRUE)

SCE.ISQ.S3 <- metafor::rma.mv(yi = es, V = V.SCE.S3, 
                               data = dat.meta.S3, 
                               mods = ~ emot_spec - 1)

res.SCE.S3 <- data.frame(clubSandwich::coef_test(SCE.S3, vcov = "CR2", cluster = dat.meta.S3$ID_study)) # , cluster = df.ES$researchgroup
res.SCE.ci.S3 = data.frame(clubSandwich::conf_int(SCE.S3, vcov = "CR2", cluster = dat.meta.S3$ID_study))
res.SCE.S3$emot_spec <- gsub("emot_spec", "", row.names(res.SCE.S3))
res.SCE.ci.S3$emot_spec <- gsub("emot_spec", "", row.names(res.SCE.ci.S3))
res.SCE.S3 = dplyr::left_join(res.SCE.S3, res.SCE.ci.S3)
## Joining, by = c("beta", "SE", "df", "emot_spec")
res.SCE.S3$I2 = het(SCE.S3, SCE.ISQ.S3)
res.SCE.clean.S3 = subset(res.SCE.S3, SE > 0.000001)

4.5.2 Table

dat_emot$emot_spec = dat_emot$nom_sousdim_clean
res_S3 <- left_join(res.SCE.clean.S3, dat_emot)
## Joining, by = "emot_spec"
res_S3[,c("beta", "SE", "tstat", "df", "p_Satt", "CI_L", "CI_U", "I2", "n_studies",    "n_nexp_out" , "n_exp_out")] <- apply(res_S3[,c("beta", "SE", "tstat", "df", "p_Satt", "CI_L", "CI_U", "I2", "n_studies",    "n_nexp_out" , "n_exp_out")], 2, function(x) round(x, 3))
DT::datatable(res_S3, 
              rownames = FALSE,
              options = list(  # options
                scrollX = TRUE,
                dom = c('ft'), 
                autoWidth = TRUE,
                columnDefs = list(
                  list(className = 'dt-center', 
                                     targets = "_all"))))

4.5.3 Forest plot

res_S3$raw_outcome <- gsub(r"{\s*\([^\)]+\)}","",
                            as.character(res_S3$nom_sousdim_clean))
tab.plot.S3 <- data.frame(
  Outcome = do.call(rbind, lapply(res_S3$nom_sousdim_clean, 
                                  function(x) paste(strwrap(x, width = 60), 
                                                    collapse = "\n"))),
  n_ADHD = res_S3$n_exp_out,
  n_nexpT = res_S3$n_nexp_out,
  n_studies = res_S3$n_studies,
  I2 = paste0(round(res_S3$I2), "%"))

value_num_plot_S3 = data.frame(apply(res_S3[, c("beta", "SE")], 2, function(x) as.numeric(as.character(x))))

forest_modif(x = value_num_plot_S3[ ,c("beta", "SE")], 
           variant = "classic",
           col = "Greys", xlab = "SMD", annotate_CI = TRUE,
           study_table = tab.plot.S3,
           group = res_S3$raw_outcome,
           type = "study_only",
           text_size = 3.5,
           x_limit = c(-1, 2),
           N = tab.plot.S3$n_ADHD + tab.plot.S3$n_nexpT,
           x_breaks = seq(-3, 3, 1)
           )

4.6 S6. Effect of age

4.6.1 a. Age

dat.meta.S6 = subset(dat.meta, !is.na(age) & outcome_RDoC %in% unique(synth_n$outcome_RDoC[synth_n$nstudy1 > 20]))
V.SCE.S6  <- with(dat.meta.S6,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study, 
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = outcome_RDoC))


SCE.S6 <- metafor::rma.mv(yi = es, V = V.SCE.S6, 
                          data = dat.meta.S6, 
                          mods = ~ age * outcome_RDoC,
                          random = ~ outcome_RDoC | ID_study,
                          struct = "CS",
                          sparse = TRUE)
clubSandwich::coef_test(SCE.S6, vcov = "CR2", cluster = dat.meta.S6$ID_study)
##                                                              Coef.  Estimate
## 1                                                          intrcpt  1.476497
## 2                                                              age -0.024798
## 3     outcome_RDoCReception of facial communication (non-adjusted) -0.596185
## 4           outcome_RDoCUnderstanding mental states (non-adjusted) -0.269615
## 5 age:outcome_RDoCReception of facial communication (non-adjusted) -0.000361
## 6       age:outcome_RDoCUnderstanding mental states (non-adjusted) -0.014946
##       SE   t-stat d.f. p-val (Satt) Sig.
## 1 0.7772  1.89982 20.6       0.0716    .
## 2 0.0746 -0.33238 17.8       0.7435     
## 3 0.8212 -0.72599 30.1       0.4734     
## 4 1.0406 -0.25908 35.8       0.7971     
## 5 0.0774 -0.00466 23.5       0.9963     
## 6 0.0985 -0.15169 31.0       0.8804
anova(SCE.S6, btt=5:6)
## 
## Test of Moderators (coefficients 5:6):
## QM(df = 2) = 0.1452, p-val = 0.9300
ggplot(dat.meta.S6, aes(x = age, y = es)) +
    facet_wrap(~outcome_RDoC) +
    geom_point(size = 2, alpha = 0.2) + 
    geom_smooth(method ="lm") +
    theme_bw()

4.6.2 a. Age diff

dat.meta.S6 = subset(dat.meta, !is.na(age_diff) & outcome_RDoC %in% unique(synth_n$outcome_RDoC[synth_n$nstudy1 > 20]))
V.SCE.S6  <- with(dat.meta.S6,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study, 
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = outcome_RDoC))


SCE.S6 <- metafor::rma.mv(yi = es, V = V.SCE.S6, 
                          data = dat.meta.S6, 
                          mods = ~ age_diff * outcome_RDoC,
                          random = ~ outcome_RDoC | ID_study,
                          struct = "CS",
                          sparse = TRUE)
clubSandwich::coef_test(SCE.S6, vcov = "CR2", cluster = dat.meta.S6$ID_study)
##                                                                   Coef.
## 1                                                               intrcpt
## 2                                                              age_diff
## 3          outcome_RDoCReception of facial communication (non-adjusted)
## 4                outcome_RDoCUnderstanding mental states (non-adjusted)
## 5 age_diff:outcome_RDoCReception of facial communication (non-adjusted)
## 6       age_diff:outcome_RDoCUnderstanding mental states (non-adjusted)
##    Estimate     SE   t-stat  d.f. p-val (Satt) Sig.
## 1  1.220131 0.0775 15.74581 80.80       <0.001  ***
## 2 -0.055853 0.2258 -0.24735  3.53        0.818     
## 3 -0.607525 0.1038 -5.85216 60.95       <0.001  ***
## 4 -0.442129 0.1089 -4.05916 79.15       <0.001  ***
## 5 -0.023296 0.2383 -0.09778  5.13        0.926     
## 6 -0.000397 0.2545 -0.00156  5.46        0.999
anova(SCE.S6, btt=5:6)
## 
## Test of Moderators (coefficients 5:6):
## QM(df = 2) = 0.2707, p-val = 0.8734
ggplot(dat.meta.S6, aes(x = age_diff, y = es)) +
    facet_wrap(~outcome_RDoC) +
    geom_point(size = 2, alpha = 0.2) + 
    geom_smooth(method ="lm") +
    theme_bw()

4.7 S7. Effect of comorbidities

4.8 CATEGORISATION ASD QUESTION

4.8.1 a. ASD

dat.meta.S7_a = subset(dat.meta, !is.na(percentage_asd) & outcome_RDoC %in% unique(synth_n$outcome_RDoC[synth_n$nstudy1 > 20]))
dat.meta.S7_a$percentage_asd = as.numeric(as.character(dat.meta.S7_a$percentage_asd))
V.SCE.S7_a  <- with(dat.meta.S7_a,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study, 
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = outcome_RDoC))


SCE.S7_a <- metafor::rma.mv(yi = es, V = V.SCE.S7_a, 
                          data = dat.meta.S7_a, 
                          mods = ~ percentage_asd * outcome_RDoC,
                          random = ~ outcome_RDoC | ID_study,
                          struct = "CS",
                          sparse = TRUE)
clubSandwich::coef_test(SCE.S7_a, vcov = "CR2", cluster = dat.meta.S7_a$ID_study)
##                                                                         Coef.
## 1                                                                     intrcpt
## 2                                                              percentage_asd
## 3                outcome_RDoCReception of facial communication (non-adjusted)
## 4                      outcome_RDoCUnderstanding mental states (non-adjusted)
## 5 percentage_asd:outcome_RDoCReception of facial communication (non-adjusted)
## 6       percentage_asd:outcome_RDoCUnderstanding mental states (non-adjusted)
##   Estimate      SE t-stat  d.f. p-val (Satt) Sig.
## 1   1.3629 0.09600  14.20 47.55      < 0.001  ***
## 2   0.0106 0.00218   4.84  4.64      0.00574   **
## 3  -0.7919 0.12063  -6.56 34.69      < 0.001  ***
## 4  -0.6442 0.13167  -4.89 42.75      < 0.001  ***
## 5  -0.0098 0.00218  -4.49  2.61      0.02746    *
## 6  -0.0075 0.00250  -3.00  3.48      0.04758    *
anova(SCE.S7_a, btt=5:6)
## 
## Test of Moderators (coefficients 5:6):
## QM(df = 2) = 188.3760, p-val < .0001
SCE.S7_a_ph = metafor::rma.mv(yi = es, V = V.SCE.S7_a, 
                data = dat.meta.S7_a, 
                mods = ~ percentage_asd : outcome_RDoC - 1,
                random = ~ outcome_RDoC | ID_study,
                struct = "CS",
                sparse = TRUE)
SCE.S7_a_ph
## 
## Multivariate Meta-Analysis Model (k = 372; method: REML)
## 
## Variance Components:
## 
## outer factor: ID_study     (nlvls = 76)
## inner factor: outcome_RDoC (nlvls = 3)
## 
##             estim    sqrt  fixed 
## tau^2      1.4117  1.1882     no 
## rho        0.7647             no 
## 
## Test for Residual Heterogeneity:
## QE(df = 369) = 8126.5346, p-val < .0001
## 
## Test of Moderators (coefficients 1:3):
## QM(df = 3) = 493.2660, p-val < .0001
## 
## Model Results:
## 
##                                                                              estimate 
## percentage_asd:outcome_RDoCMixed social processes (non-adjusted)               0.0107 
## percentage_asd:outcome_RDoCReception of facial communication (non-adjusted)    0.0008 
## percentage_asd:outcome_RDoCUnderstanding mental states (non-adjusted)          0.0031 
##                                                                                  se 
## percentage_asd:outcome_RDoCMixed social processes (non-adjusted)             0.0005 
## percentage_asd:outcome_RDoCReception of facial communication (non-adjusted)  0.0006 
## percentage_asd:outcome_RDoCUnderstanding mental states (non-adjusted)        0.0005 
##                                                                                 zval 
## percentage_asd:outcome_RDoCMixed social processes (non-adjusted)             21.3841 
## percentage_asd:outcome_RDoCReception of facial communication (non-adjusted)   1.2724 
## percentage_asd:outcome_RDoCUnderstanding mental states (non-adjusted)         5.8903 
##                                                                                pval 
## percentage_asd:outcome_RDoCMixed social processes (non-adjusted)             <.0001 
## percentage_asd:outcome_RDoCReception of facial communication (non-adjusted)  0.2032 
## percentage_asd:outcome_RDoCUnderstanding mental states (non-adjusted)        <.0001 
##                                                                                ci.lb 
## percentage_asd:outcome_RDoCMixed social processes (non-adjusted)              0.0097 
## percentage_asd:outcome_RDoCReception of facial communication (non-adjusted)  -0.0004 
## percentage_asd:outcome_RDoCUnderstanding mental states (non-adjusted)         0.0020 
##                                                                               ci.ub 
## percentage_asd:outcome_RDoCMixed social processes (non-adjusted)             0.0117 
## percentage_asd:outcome_RDoCReception of facial communication (non-adjusted)  0.0019 
## percentage_asd:outcome_RDoCUnderstanding mental states (non-adjusted)        0.0041 
##  
## percentage_asd:outcome_RDoCMixed social processes (non-adjusted)             *** 
## percentage_asd:outcome_RDoCReception of facial communication (non-adjusted) 
## percentage_asd:outcome_RDoCUnderstanding mental states (non-adjusted)        *** 
## 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
clubSandwich::coef_test(SCE.S7_a_ph, vcov = "CR2", cluster = dat.meta.S7_a$ID_study)
##                                                                         Coef.
## 1            percentage_asd:outcome_RDoCMixed social processes (non-adjusted)
## 2 percentage_asd:outcome_RDoCReception of facial communication (non-adjusted)
## 3       percentage_asd:outcome_RDoCUnderstanding mental states (non-adjusted)
##   Estimate       SE t-stat d.f. p-val (Satt) Sig.
## 1 0.010722 2.23e-03   4.81 4.56      0.00616   **
## 2 0.000757 5.06e-05  14.95 1.00      0.04252    *
## 3 0.003064 1.70e-03   1.80 1.23      0.28520
ggplot(dat.meta.S7_a, aes(x = percentage_asd, y = es)) +
    facet_wrap(~outcome_RDoC) +
    geom_point(size = 2, alpha = 0.2) + 
    geom_smooth(method ="lm") +
    theme_bw()

4.8.2 b. ODD/CD

dat.meta.S7_b = subset(dat.meta, !is.na(percentage_cd_odd) & outcome_RDoC %in% unique(synth_n$outcome_RDoC[synth_n$nstudy1 > 20]))
dat.meta.S7_b$percentage_cd_odd = as.numeric(as.character(dat.meta.S7_b$percentage_cd_odd))
V.SCE.S7_b  <- with(dat.meta.S7_b,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study, 
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = outcome_RDoC))


SCE.S7_b <- metafor::rma.mv(yi = es, V = V.SCE.S7_b, 
                          data = dat.meta.S7_b, 
                          mods = ~ percentage_cd_odd * outcome_RDoC,
                          random = ~ outcome_RDoC | ID_study,
                          struct = "CS",
                          sparse = TRUE)
clubSandwich::coef_test(SCE.S7_b, vcov = "CR2", cluster = dat.meta.S7_b$ID_study)
##                                                                            Coef.
## 1                                                                        intrcpt
## 2                                                              percentage_cd_odd
## 3                   outcome_RDoCReception of facial communication (non-adjusted)
## 4                         outcome_RDoCUnderstanding mental states (non-adjusted)
## 5 percentage_cd_odd:outcome_RDoCReception of facial communication (non-adjusted)
## 6       percentage_cd_odd:outcome_RDoCUnderstanding mental states (non-adjusted)
##   Estimate      SE t-stat  d.f. p-val (Satt) Sig.
## 1  1.20328 0.12758   9.43 34.75      < 0.001  ***
## 2  0.00372 0.00248   1.50  1.22      0.34049     
## 3 -0.54279 0.16076  -3.38 45.03      0.00152   **
## 4 -0.35872 0.16364  -2.19 46.18      0.03344    *
## 5 -0.00382 0.00275  -1.39  1.83      0.30917     
## 6 -0.00459 0.00266  -1.72  1.69      0.24909
anova(SCE.S7_b, btt=5:6)
## 
## Test of Moderators (coefficients 5:6):
## QM(df = 2) = 19.4782, p-val < .0001
SCE.S7_b_ph = metafor::rma.mv(yi = es, V = V.SCE.S7_b, 
                data = dat.meta.S7_b, 
                mods = ~ percentage_cd_odd : outcome_RDoC - 1,
                random = ~ outcome_RDoC | ID_study,
                struct = "CS",
                sparse = TRUE)
clubSandwich::coef_test(SCE.S7_b_ph, vcov = "CR2", cluster = dat.meta.S7_b$ID_study)
##                                                                            Coef.
## 1            percentage_cd_odd:outcome_RDoCMixed social processes (non-adjusted)
## 2 percentage_cd_odd:outcome_RDoCReception of facial communication (non-adjusted)
## 3       percentage_cd_odd:outcome_RDoCUnderstanding mental states (non-adjusted)
##    Estimate      SE  t-stat d.f. p-val (Satt) Sig.
## 1  0.004281 0.00180  2.3812 1.17        0.223     
## 2 -0.000039 0.00120 -0.0325 2.32        0.977     
## 3 -0.000671 0.00106 -0.6325 1.31        0.619
ggplot(dat.meta.S7_b, aes(x = percentage_cd_odd, y = es)) +
    facet_wrap(~outcome_RDoC) +
    geom_point(size = 2, alpha = 0.2) + 
    geom_smooth(method ="lm") +
    theme_bw()

4.9 S8. Effect of sex

4.10 SEX VALUE SUP 100 et aucune val > 50

dat.meta.S8 = subset(dat.meta, !is.na(sex) & outcome_RDoC %in% unique(synth_n$outcome_RDoC[synth_n$nstudy1 > 20]))
dat.meta.S8$sex = as.numeric(as.character(dat.meta.S8$sex))
dat.meta.S8$sex[dat.meta.S8$sex > 100] <- NA
V.SCE.S8  <- with(dat.meta.S8,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study, 
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = outcome_RDoC))


SCE.S8 <- metafor::rma.mv(yi = es, V = V.SCE.S8, 
                          data = dat.meta.S8, 
                          mods = ~ sex * outcome_RDoC,
                          random = ~ outcome_RDoC | ID_study,
                          struct = "CS",
                          sparse = TRUE)
clubSandwich::coef_test(SCE.S8, vcov = "CR2", cluster = dat.meta.S8$ID_study)
##                                                              Coef. Estimate
## 1                                                          intrcpt  1.37576
## 2                                                              sex -0.00555
## 3     outcome_RDoCReception of facial communication (non-adjusted) -0.84201
## 4           outcome_RDoCUnderstanding mental states (non-adjusted) -0.55380
## 5 sex:outcome_RDoCReception of facial communication (non-adjusted)  0.00797
## 6       sex:outcome_RDoCUnderstanding mental states (non-adjusted)  0.00397
##        SE t-stat  d.f. p-val (Satt) Sig.
## 1 0.17699  7.773 25.55      < 0.001  ***
## 2 0.00589 -0.943  6.05      0.38199     
## 3 0.24797 -3.396 14.52      0.00416   **
## 4 0.21692 -2.553 24.60      0.01728    *
## 5 0.00887  0.899  6.98      0.39886     
## 6 0.00660  0.601 10.69      0.56020
anova(SCE.S8, btt=5:6)
## 
## Test of Moderators (coefficients 5:6):
## QM(df = 2) = 2.9956, p-val = 0.2236
ggplot(dat.meta.S8, aes(x = sex, y = es)) +
    facet_wrap(~outcome_RDoC) +
    geom_point(size = 2, alpha = 0.2) + 
    geom_smooth(method ="lm") +
    theme_bw()

4.11 S9. Effect of IQ

4.11.1 a. IQ

dat.meta.S9 = subset(dat.meta, !is.na(iq) & outcome_RDoC %in% unique(synth_n$outcome_RDoC[synth_n$nstudy1 > 20]))
dat.meta.S9$iq = as.numeric(as.character(dat.meta.S9$iq))
# dat.meta.S9$iq[dat.meta.S9$iq > 100] <- NA
V.SCE.S9  <- with(dat.meta.S9,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study, 
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = outcome_RDoC))


SCE.S9 <- metafor::rma.mv(yi = es, V = V.SCE.S9, 
                          data = dat.meta.S9, 
                          mods = ~ iq * outcome_RDoC,
                          random = ~ outcome_RDoC | ID_study,
                          struct = "CS",
                          sparse = TRUE)
clubSandwich::coef_test(SCE.S9, vcov = "CR2", cluster = dat.meta.S9$ID_study)
##                                                             Coef. Estimate
## 1                                                         intrcpt -0.62179
## 2                                                              iq  0.01834
## 3    outcome_RDoCReception of facial communication (non-adjusted)  1.49681
## 4          outcome_RDoCUnderstanding mental states (non-adjusted) -1.53908
## 5 iq:outcome_RDoCReception of facial communication (non-adjusted) -0.02173
## 6       iq:outcome_RDoCUnderstanding mental states (non-adjusted)  0.00867
##       SE  t-stat d.f. p-val (Satt) Sig.
## 1 6.3577 -0.0978 5.77        0.925     
## 2 0.0610  0.3006 5.95        0.774     
## 3 6.2629  0.2390 7.97        0.817     
## 4 8.0869 -0.1903 5.21        0.856     
## 5 0.0600 -0.3621 7.92        0.727     
## 6 0.0772  0.1123 5.02        0.915
anova(SCE.S9, btt=5:6)
## 
## Test of Moderators (coefficients 5:6):
## QM(df = 2) = 1.9952, p-val = 0.3688
ggplot(dat.meta.S9, aes(x = iq, y = es)) +
    facet_wrap(~outcome_RDoC) +
    geom_point(size = 2, alpha = 0.2) + 
    geom_smooth(method ="lm") +
    theme_bw()

4.11.2 b. IQ diff

dat.meta.S9 = subset(dat.meta, !is.na(iq_diff) & outcome_RDoC %in% unique(synth_n$outcome_RDoC[synth_n$nstudy1 > 20]))
dat.meta.S9$iq_diff = as.numeric(as.character(dat.meta.S9$iq_diff))


SCE.S9 <- metafor::rma.mv(yi = es, V = V.SCE.S9, 
                          data = dat.meta.S9, 
                          mods = ~ iq_diff * outcome_RDoC,
                          random = ~ outcome_RDoC | ID_study,
                          struct = "CS",
                          sparse = TRUE)
clubSandwich::coef_test(SCE.S9, vcov = "CR2", cluster = dat.meta.S9$ID_study)
##                                                                  Coef. Estimate
## 1                                                              intrcpt  1.35216
## 2                                                              iq_diff  0.00915
## 3         outcome_RDoCReception of facial communication (non-adjusted) -0.81242
## 4               outcome_RDoCUnderstanding mental states (non-adjusted) -0.59370
## 5 iq_diff:outcome_RDoCReception of facial communication (non-adjusted) -0.01254
## 6       iq_diff:outcome_RDoCUnderstanding mental states (non-adjusted)  0.00430
##       SE  t-stat  d.f. p-val (Satt) Sig.
## 1 0.3691  3.6629 29.78       <0.001  ***
## 2 0.0398  0.2301  5.81       0.8259     
## 3 0.3572 -2.2744 24.99       0.0318    *
## 4 0.4304 -1.3795 22.01       0.1816     
## 5 0.0426 -0.2943  3.20       0.7866     
## 6 0.0484  0.0887  5.75       0.9323
anova(SCE.S9, btt=5:6)
## 
## Test of Moderators (coefficients 5:6):
## QM(df = 2) = 1.6636, p-val = 0.4353
ggplot(dat.meta.S9, aes(x = iq_diff, y = es)) +
    facet_wrap(~outcome_RDoC) +
    geom_point(size = 2, alpha = 0.2) + 
    geom_smooth(method ="lm") +
    theme_bw()

4.12 S10. Effect of rob

dat.meta.S10 = subset(dat.meta, !is.na(rob_tot) & outcome_RDoC %in% unique(synth_n$outcome_RDoC[synth_n$nstudy1 > 20]))
V.SCE.S10  <- with(dat.meta.S10,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study, 
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = outcome_RDoC))


SCE.S10 <- metafor::rma.mv(yi = es, V = V.SCE.S10, 
                          data = dat.meta.S10, 
                          mods = ~ rob_tot * outcome_RDoC,
                          random = ~ outcome_RDoC | ID_study,
                          struct = "CS",
                          sparse = TRUE)
clubSandwich::coef_test(SCE.S10, vcov = "CR2", cluster = dat.meta.S10$ID_study)
##                                                                  Coef. Estimate
## 1                                                              intrcpt  0.79485
## 2                                                              rob_tot  0.07323
## 3         outcome_RDoCReception of facial communication (non-adjusted) -0.64818
## 4               outcome_RDoCUnderstanding mental states (non-adjusted) -0.06789
## 5 rob_tot:outcome_RDoCReception of facial communication (non-adjusted)  0.00139
## 6       rob_tot:outcome_RDoCUnderstanding mental states (non-adjusted) -0.06304
##       SE t-stat  d.f. p-val (Satt) Sig.
## 1 0.1524  5.217  5.66      0.00236   **
## 2 0.0238  3.074  4.50      0.03174    *
## 3 0.3548 -1.827 18.86      0.08359    .
## 4 0.2919 -0.233  5.20      0.82499     
## 5 0.0607  0.023 18.37      0.98192     
## 6 0.0455 -1.386  4.61      0.22900
anova(SCE.S10, btt=5:6)
## 
## Test of Moderators (coefficients 5:6):
## QM(df = 2) = 2.3662, p-val = 0.3063
ggplot(dat.meta.S10, aes(x = rob_tot, y = es)) +
    facet_wrap(~outcome_RDoC) +
    geom_point(size = 2, alpha = 0.2) + 
    geom_smooth(method ="lm") +
    theme_bw()

Reception of facial communication (non-adjusted) Understanding mental states (non-adjusted) Mixed social processes (non-adjusted)

4.13 S11. Effect of adjustment

dat.meta.S11 = subset(dat.meta, !is.na(outcome_RDoC_agg) & !is.na(es_adj) & outcome_RDoC_agg %in% c("Understanding mental states", "Mixed social processes", "Reception of facial communication"))
V.SCE.S11  <- with(dat.meta.S11,
  clubSandwich::impute_covariance_matrix(
    vi = se^2, 
    cluster = ID_study, 
    r = 0.8,
    return_list = FALSE,
    smooth_vi = TRUE, 
    subgroup = outcome_RDoC))


SCE.S11 <- metafor::rma.mv(yi = es, V = V.SCE.S11, 
                          data = dat.meta.S11, 
                          mods = ~ outcome_RDoC_agg * es_adj,
                          random = ~ outcome_RDoC | ID_study,
                          struct = "CS",
                          sparse = TRUE)
clubSandwich::coef_test(SCE.S11, vcov = "CR2", cluster = dat.meta.S11$ID_study)
##                                                                  Coef. Estimate
## 1                                                              intrcpt    1.356
## 2                    outcome_RDoC_aggReception of facial communication   -0.807
## 3                          outcome_RDoC_aggUnderstanding mental states   -0.600
## 4                                                   es_adjNon-Adjusted   -0.122
## 5 outcome_RDoC_aggReception of facial communication:es_adjNon-Adjusted    0.185
## 6       outcome_RDoC_aggUnderstanding mental states:es_adjNon-Adjusted    0.145
##      SE t-stat  d.f. p-val (Satt) Sig.
## 1 0.200  6.797  7.06      < 0.001  ***
## 2 0.201 -4.019 10.02      0.00243   **
## 3 0.211 -2.846  8.09      0.02137    *
## 4 0.209 -0.585  7.89      0.57481     
## 5 0.220  0.842 12.30      0.41611     
## 6 0.235  0.618 10.28      0.55015
anova(SCE.S11, btt=5:6)
## 
## Test of Moderators (coefficients 5:6):
## QM(df = 2) = 0.4862, p-val = 0.7842
ggplot(dat.meta.S11, aes(x = es_adj, y = es)) +
    facet_wrap(~outcome_RDoC_agg) +
    geom_point(size = 2, alpha = 0.2) + 
    geom_boxplot(alpha = 0.2) + 
    geom_smooth(method ="lm") +
    theme_bw()